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probability density
This term is a technical concept used exclusively in statistics and probability theory. It describes the relative likelihood of a continuous random variable, distinguishing it from a probability mass function, which is used for discrete variables. Because it deals with continuous ranges, the value of the density at a single point does not represent a probability itself, but rather the rate of change of the probability.
In practical application, the term is almost always paired with "function" (probability density function or PDF). It is an uncountable noun in this mathematical context, as it refers to a conceptual property or a specific mathematical function rather than a countable object.
Meanings
A function that describes the relative likelihood for a continuous random variable to take on a given value, where the area under the curve over an interval represents the probability of the variable falling within that interval.
The probability density of a normal distribution is represented by a bell-shaped curve.
Examples
The area under the curve of the probability density function represents the total probability.
We need to calculate the probability density at this specific point to understand the distribution.
Wait, does the probability density have to be positive for all values of x?
The probability density of a normal distribution forms a characteristic bell shape.
The probability density of a normal distribution forms a characteristic bell shape.
I wonder if the probability density shifts when we change the mean of the sample.
The professor explained how probability density differs from a discrete probability mass function.
The professor explained how probability density differs from a discrete probability mass function.
Integrating the probability density over the entire range must equal one.
Let us examine the probability density of the error terms in this linear model.